Following scenario:
A group of participants was behaviorally tested before and after a certain manipulation (pre-post-design, no control group), but at both points in times other factors where manipulated too (e.g., 2x2 within-subjects experimental factors at T1 and T2).
The manipulation itself was accompanied by the measurement of a continuous variable (indicating e.g., the perception of/immediate response to the manipulation/event).
Hence, this is a differential-psychological experiment that does not compare an experimental and control group, but analyzing different levels (e.g., strengths) of the pre-post manipulation. A control group can not have this response in the absence of pre-post manipulation and is also not needed as the manipulation results itself in varying degrees of responses.
How can one analyze the pre-post changes depending on/associated with this continuous variable accounting also for the 2x2 experimental factors?
If the latter 2x2 factors would not exist, one could for instance calculate a simple correlation/regression between the continuous variable (associated with the manipulation in-between) and the pre-post difference scores.
However, in this more complex model I thought about using a GLM on the difference/gain scores (reflecting the pre-post change) including the 2x2 within-subject factors and the between-subject continuous variable.
A between-subject effect or within/between-interaction effects would indicate that the continuous variable (associated/characterizing the manipulation between pre-post) would predict change.
Would you consider this approach appropriate?
I strongly urge you to use the Analysis of Covariance (ANCOVA) for this type of data. The reasons are many, but an ANOVA is not applicable, moreover, you are attempting to normalize your data by pre and post testing conditions; thus, an ANCOVA is designed for such experiments.
Thank you very much for your thoughts.
Are you referring to the pre-values as covariates in the ANCOVA (although I am not familiar with the procedure to allocate the 2x2 covariates [pre-values of the 2x2 within-subject factors] separately to their 2x2 post-scores and at the same time analyzing also the effect of the continuous covariate of interest) or do you mean only the continuous measure associated with the pre-post manipulation as "covariate" (in fact that would be then the GLM I referred to)?
Why is an ANOVA not applicable in your point of view (an ANOVA on differences scores is considered a valid alternative to an ANCOVA sometimes)?
If this is a within-repeated subjects design, then usually, the first data point is taken to determine the "control" conditions. In an ANCOVA, you are testing before and after effects. There are many reasons why an ANOVA is not applicable, I refer you to Ostle's "Statistics in Research" for further, more detailed information. Summarily, homoscedasticity is not satisfied...
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